Bayesian data augmentation is a suitable method for estimation using
this extended likelihood. Here, values for
\(\text{$z$}\)  are generated in an MCMC sampling scheme to evaluate an “augmented posterior”
proportional to the extended likelihood
multiplied by a parameter prior. This has been used to estimate the elliptical
and skew elliptical copulas discussed in Section  below. For example,
[1]} do so
for a Gaussian copula, while [2]} do so for the \(t\)  copula, and [3]} for the skew \(t\)  copula. [4]} considered
the extended likelihood above using empirical marginals and rank data, [2]} and [6]}
provide early applications to higher dimensional Gaussian \(F_Z\) . Last, the multivariate probit model is a
Gaussian copula model, and the popular approach of [7]} is a special case of these data augmentation algorithms.
